The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

The aim of this study is to reveal and evaluate the attending and interpreting skills of student thinking of prospective teachers, as well as their instructional suggestions as responding skills. The current study was conducted with 29 prospective mathematics teachers (PMTs) within a qualitative design in the context of probability. First, three…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

This essay highlights the value of an applied methodology course in program evaluation in the education doctorate program by exploring several benefits that it offers to enhance a doctoral student's ability to solve complex problems of practice. Observations and recommendations are made based on designing and teaching two cohorts of EdD students…

This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

We report the design of an analog technology, what we refer to as a SunRule, that uses sunlight to model multiplication. Physical models that explore multiplication are fixtures in elementary mathematics classrooms. Our interest in physical models of multiplication was driven by an overarching design problem: How could a physical tool realize a…

Mathematics and science have similar learning processes (SLPs) and it has been proposed that courses focused on these and other similarities promote transfer across disciplines. However, it is not known how the use of these processes in lessons taught to children change throughout a preservice teacher education course or which are most likely to…

Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is "embodied" -- inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building…

Recently, attention has focused on identifying core instructional practices that could leverage novice teachers' development of professional knowledge and skill. To help novices learn to implement these practices, there is also increasing interest in developing enactment tools that could translate abstract conceptual tasks into more concrete…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

Teaching computer science (CS) in high schools, rather than just programming or even computer literacy, is important as a means of introducing students to the true nature of CS, and enhancing their problem-solving skills. Since teachers are the key to the success of any high school educational initiative, any discussion of high school programs…

Nineteen pre-service and in-service teachers taking a chemistry teaching methods course at a university in Hong Kong were asked to take a diagnostic assessment. It consisted of seven multiple-choice questions about the chemistry of the lead-acid battery. Analysis of the teachers' responses to the questions indicated that they had difficulty in…

This study identified the problem solving strategies used by students within a university course designed to teach pre-service teachers educational technology, and whether those strategies were influenced by the format of the course (i.e., face-to-face computer lab vs. online). It also examined to what extent the type of problem solving strategies…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

Discusses the need for preservice elementary teachers to experience inquiry first-hand, suggesting that they engage in problem-solving rather than just "talking about" it. A typical teacher education program is described with suggestions to incorporate inquiry-oriented experiences. An inquiry-oriented activity using sand and funnels is included.…